ModularField(R, Mod, reduction, merge, exactQuo)ΒΆ
modring.spad line 187 [edit on github]
Mod: AbelianMonoid
reduction: (R, Mod) -> R
merge: (Mod, Mod) -> Union(Mod, failed)
exactQuo: (R, R, Mod) -> Union(R, failed)
These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See ModularRing, EuclideanModularRing
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from Magma
- *: (%, Fraction Integer) -> %
from RightModule Fraction Integer
- *: (Fraction Integer, %) -> %
from LeftModule Fraction Integer
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- ^: (%, Integer) -> %
from DivisionRing
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- coerce: % -> %
from Algebra %
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: % -> R
coerce(x)undocumented- coerce: Fraction Integer -> %
- coerce: Integer -> %
from NonAssociativeRing
- commutator: (%, %) -> %
from NonAssociativeRng
- divide: (%, %) -> Record(quotient: %, remainder: %)
from EuclideanDomain
- euclideanSize: % -> NonNegativeInteger
from EuclideanDomain
- expressIdealMember: (List %, %) -> Union(List %, failed)
from PrincipalIdealDomain
- exQuo: (%, %) -> Union(%, failed)
exQuo(x, y)undocumented
- exquo: (%, %) -> Union(%, failed)
from EntireRing
- extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)
from EuclideanDomain
- extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)
from EuclideanDomain
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
from GcdDomain
- inv: % -> %
from DivisionRing
- latex: % -> String
from SetCategory
- lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)
from LeftOreRing
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- modulus: % -> Mod
modulus(x)undocumented
- multiEuclidean: (List %, %) -> Union(List %, failed)
from EuclideanDomain
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- plenaryPower: (%, PositiveInteger) -> %
- principalIdeal: List % -> Record(coef: List %, generator: %)
from PrincipalIdealDomain
- quo: (%, %) -> %
from EuclideanDomain
- recip: % -> Union(%, failed)
from MagmaWithUnit
- reduce: (R, Mod) -> %
reduce(r, m)undocumented
- rem: (%, %) -> %
from EuclideanDomain
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from AbelianMonoid
- sizeLess?: (%, %) -> Boolean
from EuclideanDomain
- squareFree: % -> Factored %
- squareFreePart: % -> %
- subtractIfCan: (%, %) -> Union(%, failed)
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
- zero?: % -> Boolean
from AbelianMonoid
Algebra %
BiModule(%, %)
BiModule(Fraction Integer, Fraction Integer)
Module %